Using an Effective Numerical Method for Solving a Class of Lane-Emden Equations

Table 4

Numerical solutions for Example 4.

𝑥	𝑢𝑇(𝑥)	𝑢50	|𝑢𝑇(𝑥)−𝑢50(𝑥)|	|𝑢^′𝑇(𝑥)−𝑢^′50(𝑥)|	|𝑢𝑇^′′(𝑥)−𝑢^′′50(𝑥)|
0.0	0	0	0	0	0.0198013
0.1	0.00499584	0.00497722	1.86175×10^−5	2.00342×10^−4	2.32373×10^−5
0.2	0.0199337	0.0198951	3.85998×10^−5	1.97876×10^−4	1.09236×10^−4
0.3	0.0446665	0.0446089	5.76023×10^−5	1.76911×10^−4	4.26393×10^−4
0.4	0.0789556	0.0788834	7.21411×10^−5	9.9302×10^−5	1.3039×10^−3
0.5	0.122479	0.122407	7.29154×10^−5	1.17118×10^−4	3.30994×10^−3
0.6	0.174846	0.174807	3.90139×10^−5	6.28561×10^−4	7.38437×10^−3
0.7	0.235604	0.235676	7.16611×10^−5	1.71224×10^−3	1.50496×10^−2
0.8	0.304261	0.304599	3.37896×10^−4	3.83982×10^−3	2.87368×10^−2
0.9	0.380294	0.381194	8.99901×10^−4	7.7914×10^−3	5.2279×10^−2
1.0	0.463163	0.465161	1.99826×10^−3	1.48297×10^−2	9.16336×10^−2